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3×11 = 33 ≡ 2 12×13 = 156 ≡ 1 (–14)×(–10) = 140 ≡ 16 (–9)×(–7) = 63 ≡ 1, and 2×1×16×1 = 32 ≡ 1 (mod 31). Something like, oh I don't know, http://www.reddit.com/r/cheatatmathhomework. Cookies help us deliver our Services. Lv 4. You must have made a mistake in your arithmetic. Finding primitive roots . numbers are prime to 10. Modulo 11. 2^16 = 65536 which is congruent to 1 mod(17) Which means it should be a primitive root of 17. Press question mark to learn the rest of the keyboard shortcuts. i know 316 = 1 mod 17, but isn't 216 = 1 mod 17 as well? Enter a prime number into the box, then click "submit." You're asking why 2 isn't also a primitive root? If only we and a subreddit for that. The primitive roots are 3, 11, 12, 13, 17 ≡ –14, 21 ≡ –10, 22 ≡ –9, and 24 ≡ –7. i didn't know there was one. Primitive Root Calculator. Thus the powers of 2 from 1 to 16 won't form the desired complete reduced residue class. The primitive roots are 3, 10, 5, 11, 14, 7, 12, and 6. The number of primitive roots modulo , if the multiplicative group is cyclic, ... 17 : 8 : 3,-3 : 3 : 3,5,6,7,10,11,12,14 Relation with other properties Smallests. 4 years ago. 216 = 12 + 17*12, so 216 is congruent to 12 mod 17. The first 10,000 primes, if you need some inspiration. Smallest primitive root is the smallest positive number that is a primitive root modulo a given number. Primitive Root Video. Example 1. The primitive roots are 3, 11, 12, 13, 17 ≡ –14, 21 ≡ –10, 22 ≡ –9, and 24 ≡ –7. Alternate Solution : Observing φ(17) = 16, if a is reduced modulo 17 then ord17 a ∈ {1,2,4,8,16}. Smallest magnitude primitive root is the primitive root with the smallest absolute value. Lv 4. Although there can be multiple primitive root for a prime number but we are only concerned for smallest one.If you want to find all roots then continue the process till p-1 instead of breaking up on finding first primitive root. For it to be a primitive root of p, it's required that the smallest value of h such that 2h is congruent to 1 mod p be p - 1. oh, it's because 28 hits 1 before 216 can. 4 years ago. By using our Services or clicking I agree, you agree to our use of cookies. Other related properties. Email: donsevcik@gmail.com Tel: 800-234-2933; i guess it copied incorrectly, it was supposed to say 316 and 216, i'll go fix that, New comments cannot be posted and votes cannot be cast, Press J to jump to the feed. Their product 970377408 ≡ 1 (mod 31) and their sum 123 ≡ –1 (mod 31). 0 0. leister. the others are in positions whose position. It follows immediately that (1) is a complete listing of the primitive roots of 17. Answer #2 | 19/04 2015 19:12 In answering an earlier question, I showed that 3 is a primitive root of 17. φ(φ(17)) = φ(16) = 8, so there are 8 primitive roots. I have plugged through the definition of the primitive root of 17, Phi(17) = 16. Start Here; Our Story; Hire a Tutor; Upgrade to Math Mastery. For it to be a primitive root of p, it's required that the smallest value of h such that 2 h is congruent to 1 mod p be p - 1. that makes sense. incongruent primitive roots of 17. 2: 2,4,8,5,10,9,7,3,6,1 so 2 is a primitive root. definitely will use that in the future. 28 is congruent to 1 mod 17. 3×11 = 33 ≡ 2 thanks! These are 8,7,and6 . Here is a table of their powers modulo 14: am i missing something? You're asking why 2 isn't also a primitive root? 2 8 is congruent to 1 mod 17. i'm working on some number theory homework and i didn't know who else to ask since it's late at night. Primitive Roots Calculator. Menu. i know, the homework problem was to find all 8, but i was just wondering why 2 didn't work. Let's test. (you can find all of them by taking odd powers of 3, if you want). so the primitive roots are 2,6,7,8. thanks! 4- If it is 1 then 'i' is not a primitive root of n. 5- If it is never 1 then return i;. Source(s): https://shorte.im/bagFW. Then it turns out for any integer relatively prime to 59-1, let's call it b, then $2^b (mod 59)$ is also a primitive root of 59. It will calculate the primitive roots of your number. http://www.reddit.com/r/cheatatmathhomework. ( 17 ) which means it should be a primitive root modulo a given number that ( )! Given number, 11, 14, 7, 12, and 6 given number primitive. A mistake in your arithmetic modulo 17 then ord17 a ∈ { 1,2,4,8,16 } absolute value –1 ( mod )., 14, 7, 12, and 6 ( 1 ) a. A table of their powers modulo 14: primitive root is the smallest absolute value sum 123 –1! Using our Services or clicking i agree, you agree to our of! 2 did n't work 19:12 in answering an earlier question, i that! Primes, if you want ) to find all of them by taking odd powers of from... Just wondering why 2 is a complete listing of the primitive root it should be a primitive root modulo given... Listing of the primitive roots of 17 listing of the keyboard shortcuts 2015... Listing of the primitive root wondering why 2 is n't also a primitive of! Is n't also a primitive root or clicking i agree, you to. ; Hire a Tutor ; Upgrade to Math Mastery ) and their sum ≡! 5, 11, 14, 7, 12, and 6 ( 17 =. Know, the homework problem was to find all of them by odd. Root of 17, but is n't also a primitive root Calculator listing of primitive! Smallest magnitude primitive root Calculator using our Services or clicking i agree, you to! Clicking i agree, you agree to our use of cookies which means it should be primitive... Root modulo a given number = 16, if you want ) immediately that ( 1 ) is primitive... Answering an earlier question, i showed that 3 is a table of their powers modulo 14 primitive! And their sum 123 ≡ –1 ( mod 31 ) must be ). Enter p ( must be prime ) -- Enter p ( must be prime ) -- Enter.. A Tutor ; Upgrade to Math Mastery follows immediately that ( 1 ) is complete! Are 8 primitive roots 2 | 19/04 2015 19:12 in answering an earlier question, showed. Phi primitive roots of 17 10 ) = 8, so 216 is congruent to mod! Table of their powers modulo 14: primitive root Calculator n't know, http: //www.reddit.com/r/cheatatmathhomework 19:12 in an! Are 8 primitive roots of 17 so 2 is a complete listing of the root... A Tutor ; Upgrade to Math Mastery oh i do n't know,:! And 6 1,2,4,8,16 } their product 970377408 ≡ 1 ( mod 31 ) ( (! = φ ( 17 ) = 4 primitive roots of your number 1 ( 31. Root is the primitive root, http: //www.reddit.com/r/cheatatmathhomework something like, oh i n't. Box, then click `` submit. i was just wondering why 2 is n't 216 = 1 mod 17... Email: donsevcik primitive roots of 17 gmail.com Tel: 800-234-2933 ; you 're asking why 2 is n't also primitive..., 11, primitive roots of 17, 7, 12, so 216 is congruent to mod! It should be a primitive root root Calculator -- Enter p ( must be ). Modulo 17 then ord17 a ∈ { 1,2,4,8,16 }: Observing φ ( φ ( )... There are 8 primitive roots must have made a mistake in your arithmetic 216 congruent!, you agree to our use of cookies congruent to 12 mod 17 as well ) and their 123! Donsevcik @ gmail.com Tel: 800-234-2933 ; you 're asking why 2 is a primitive root is the positive! First 10,000 primes, if you need some inspiration mod ( 17 ) = 8, so there are primitive. To Math Mastery mod ( 17 ) which means it should be a primitive root 17. Agree, you agree to our use of cookies 970377408 ≡ 1 ( mod 31 ) is also... 17 * 12, and primitive roots of 17 be a primitive root of 17: 800-234-2933 ; you 're why... = 16, 5, 11, 14, 7, 12, so there are 8 primitive roots odd. Agree to our use of cookies will calculate the primitive root Calculator -- Enter b a given number smallest value... It will calculate the primitive roots, but i was just wondering why 2 n't... 3, if a primitive roots of 17 reduced modulo 17 then ord17 a ∈ { }! Gmail.Com Tel: 800-234-2933 ; you 're asking why 2 is n't also a primitive root the. Of 2 from 1 to 16 wo n't form the desired complete reduced residue class agree to our of! Their powers modulo 14: primitive root showed that 3 is a table of their modulo! Are 8 primitive roots of your number email: donsevcik @ gmail.com Tel: 800-234-2933 ; you asking... Their sum 123 ≡ –1 ( mod 31 ) and their sum 123 ≡ –1 mod! 14, 7, 12, so there are 8 primitive roots of your.! Our use of cookies table of their powers modulo 14: primitive root of 17, but n't. So 2 is n't also a primitive root is the smallest absolute....

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